MinT - Best Known (102−56, 102, s)-Nets in Base 32

Best Known (102−56, 102, s)-Nets in Base 32

(102−56, 102, 218)-Net over F₃₂ — Constructive and digital

Digital (46, 102, 218)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 35, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
2. digital (11, 67, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
      - a function field by SÃ©mirat [i]

(102−56, 102, 420)-Net over F₃₂ — Digital

Digital (46, 102, 420)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−56, 102, 513)-Net in Base 32 — Constructive

(46, 102, 513)-net in base 32, using

6 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(102−56, 102, 110823)-Net in Base 32 — Upper bound on s

There is no (46, 102, 110824)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3352 075996 653390 000415 874783 722361 723279 190004 965594 082566 958055 828293 217165 106112 423495 113050 325638 475442 410608 104535 599384 025177 054871 662546 972161 661572 > 32¹⁰² [i]