MinT - Best Known (113−75, 113, s)-Nets in Base 5

Best Known (113−75, 113, s)-Nets in Base 5

(113−75, 113, 78)-Net over F₅ — Constructive and digital

Digital (38, 113, 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]

(113−75, 113, 451)-Net in Base 5 — Upper bound on s

There is no (38, 113, 452)-net in base 5, because

1 times m-reduction [i] would yield (38, 112, 452)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1 996218 284226 485390 698331 794925 997201 689363 819120 324309 034196 001176 441228 475025 > 5¹¹² [i]