MinT - Best Known (78−63, 78, s)-Nets in Base 32

Best Known (78−63, 78, s)-Nets in Base 32

(78−63, 78, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 78, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 78, 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]

(78−63, 78, 158)-Net over F₃₂ — Digital

Digital (15, 78, 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]

(78−63, 78, 2178)-Net in Base 32 — Upper bound on s

There is no (15, 78, 2179)-net in base 32, because

1 times m-reduction [i] would yield (15, 77, 2179)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 79 708779 783661 709981 690589 371209 700432 858834 188176 997320 638857 938433 739155 558644 843126 459975 633891 157893 218279 751040 > 32⁷⁷ [i]