MinT - Best Known (43, 43+103, s)-Nets in Base 5

Best Known (43, 43+103, s)-Nets in Base 5

(43, 43+103, 78)-Net over F₅ — Constructive and digital

Digital (43, 146, 78)-net over F₅, using

t-expansion [i] based on digital (38, 146, 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+103, 84)-Net over F₅ — Digital

Digital (43, 146, 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+103, 445)-Net in Base 5 — Upper bound on s

There is no (43, 146, 446)-net in base 5, because

1 times m-reduction [i] would yield (43, 145, 446)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 241968 578379 838865 509150 987412 922418 883333 148454 668714 742216 090558 202677 194186 909596 691634 271534 716185 > 5¹⁴⁵ [i]