MinT - Best Known (98−84, 98, s)-Nets in Base 32

Best Known (98−84, 98, s)-Nets in Base 32

(98−84, 98, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 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]

(98−84, 98, 146)-Net over F₃₂ — Digital

Digital (14, 98, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(98−84, 98, 1709)-Net in Base 32 — Upper bound on s

There is no (14, 98, 1710)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3209 044062 412225 933481 227500 394186 623206 040103 302153 011729 003911 065442 094845 041518 897591 068362 002860 974917 526150 436745 923916 989408 163239 529910 982870 > 32⁹⁸ [i]