MinT - Best Known (43, 43+107, s)-Nets in Base 5

Best Known (43, 43+107, s)-Nets in Base 5

(43, 43+107, 78)-Net over F₅ — Constructive and digital

Digital (43, 150, 78)-net over F₅, using

t-expansion [i] based on digital (38, 150, 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+107, 84)-Net over F₅ — Digital

Digital (43, 150, 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+107, 436)-Net in Base 5 — Upper bound on s

There is no (43, 150, 437)-net in base 5, because

1 times m-reduction [i] would yield (43, 149, 437)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 141 230088 933031 102733 262200 586883 161905 895162 996967 695551 681511 755492 091322 518813 284755 799410 619739 311685 > 5¹⁴⁹ [i]