MinT - Best Known (43, 43+47, s)-Nets in Base 5

Best Known (43, 43+47, s)-Nets in Base 5

(43, 43+47, 78)-Net over F₅ — Constructive and digital

Digital (43, 90, 78)-net over F₅, using

t-expansion [i] based on digital (38, 90, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(43, 43+47, 84)-Net over F₅ — Digital

Digital (43, 90, 84)-net over F₅, using

net from sequence [i] based on digital (43, 83)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 43 and N(F) ≥ 84, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(43, 43+47, 1177)-Net in Base 5 — Upper bound on s

There is no (43, 90, 1178)-net in base 5, because

1 times m-reduction [i] would yield (43, 89, 1178)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 162 762664 942017 029472 757806 566138 541192 703386 375843 824519 660425 > 5⁸⁹ [i]