MinT - Best Known (99−50, 99, s)-Nets in Base 5

Best Known (99−50, 99, s)-Nets in Base 5

(99−50, 99, 82)-Net over F₅ — Constructive and digital

Digital (49, 99, 82)-net over F₅, using

t-expansion [i] based on digital (48, 99, 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]

(99−50, 99, 100)-Net over F₅ — Digital

Digital (49, 99, 100)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−50, 99, 1472)-Net in Base 5 — Upper bound on s

There is no (49, 99, 1473)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1581 372972 507942 718999 976529 003948 962920 899597 642735 663970 355520 756517 > 5⁹⁹ [i]