MinT - Best Known (94−46, 94, s)-Nets in Base 5

Best Known (94−46, 94, s)-Nets in Base 5

(94−46, 94, 82)-Net over F₅ — Constructive and digital

Digital (48, 94, 82)-net over F₅, using

net from sequence [i] based on digital (48, 81)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 48 and N(F) ≥ 82, using
  - an explicitly constructive algebraic function field [i]

(94−46, 94, 106)-Net over F₅ — Digital

Digital (48, 94, 106)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(94−46, 94, 1677)-Net in Base 5 — Upper bound on s

There is no (48, 94, 1678)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 505784 306095 339777 592479 030876 087002 374336 902175 583724 485581 038425 > 5⁹⁴ [i]