MinT - Best Known (17, 17+77, s)-Nets in Base 32

Best Known (17, 17+77, s)-Nets in Base 32

(17, 17+77, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 94, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 94, 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]

(17, 17+77, 158)-Net over F₃₂ — Digital

Digital (17, 94, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 94, 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]

(17, 17+77, 2319)-Net in Base 32 — Upper bound on s

There is no (17, 94, 2320)-net in base 32, because

1 times m-reduction [i] would yield (17, 93, 2320)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 95 772566 233347 182274 388706 622870 420485 887531 944984 749540 264727 717172 450617 209720 211549 543304 431866 828794 369147 354385 210604 998009 170051 634616 > 32⁹³ [i]