MinT - Best Known (39, 39+41, s)-Nets in Base 5

Best Known (39, 39+41, s)-Nets in Base 5

(39, 39+41, 78)-Net over F₅ — Constructive and digital

Digital (39, 80, 78)-net over F₅, using

t-expansion [i] based on digital (38, 80, 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]

(39, 39+41, 80)-Net over F₅ — Digital

Digital (39, 80, 80)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(39, 39+41, 1182)-Net in Base 5 — Upper bound on s

There is no (39, 80, 1183)-net in base 5, because

1 times m-reduction [i] would yield (39, 79, 1183)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 16 600759 256928 312318 646142 033244 847935 418373 066734 121905 > 5⁷⁹ [i]