MinT - Best Known (47, 109, s)-Nets in Base 32

Best Known (47, 109, s)-Nets in Base 32

(47, 109, 202)-Net over F₃₂ — Constructive and digital

Digital (47, 109, 202)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 38, 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 (9, 71, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(47, 109, 360)-Net over F₃₂ — Digital

Digital (47, 109, 360)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 109, 513)-Net in Base 32 — Constructive

(47, 109, 513)-net in base 32, using

32¹ times duplication [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]

(47, 109, 78502)-Net in Base 32 — Upper bound on s

There is no (47, 109, 78503)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 115 188248 721396 836208 052918 040739 590699 544209 069475 994937 226387 544252 428236 155487 519150 066353 503925 127890 084582 841287 160576 696343 611359 045478 905600 279813 536243 076896 > 32¹⁰⁹ [i]