MinT - Best Known (77−61, 77, s)-Nets in Base 32

Best Known (77−61, 77, s)-Nets in Base 32

(77−61, 77, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 77, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 77, 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]

(77−61, 77, 158)-Net over F₃₂ — Digital

Digital (16, 77, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 77, 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]

(77−61, 77, 2510)-Net in Base 32 — Upper bound on s

There is no (16, 77, 2511)-net in base 32, because

1 times m-reduction [i] would yield (16, 76, 2511)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 468866 206616 618972 526014 624054 956656 483416 783253 570115 620024 766025 742067 532139 784594 198199 880233 450429 693166 897548 > 32⁷⁶ [i]