MinT - Best Known (117−79, 117, s)-Nets in Base 5

Best Known (117−79, 117, s)-Nets in Base 5

(117−79, 117, 78)-Net over F₅ — Constructive and digital

Digital (38, 117, 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]

(117−79, 117, 433)-Net in Base 5 — Upper bound on s

There is no (38, 117, 434)-net in base 5, because

1 times m-reduction [i] would yield (38, 116, 434)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1249 073882 485998 966499 912640 994595 048795 993712 704986 326146 058869 469122 692637 230825 > 5¹¹⁶ [i]