MinT - Best Known (97−81, 97, s)-Nets in Base 32

Best Known (97−81, 97, s)-Nets in Base 32

(97−81, 97, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 97, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 97, 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]

(97−81, 97, 158)-Net over F₃₂ — Digital

Digital (16, 97, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 97, 158)-net over F₃₂, using
- net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
    - an algebraic function field by Beelen and Pellikaan [i]

(97−81, 97, 2062)-Net in Base 32 — Upper bound on s

There is no (16, 97, 2063)-net in base 32, because

1 times m-reduction [i] would yield (16, 96, 2063)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 137715 431112 412218 175574 398639 276526 167795 812513 640751 410143 174475 054593 150161 983592 221131 581376 516896 360478 501751 276326 471532 397516 363230 742592 > 32⁹⁶ [i]