MinT - Best Known (50, 50+45, s)-Nets in Base 5

Best Known (50, 50+45, s)-Nets in Base 5

(50, 50+45, 82)-Net over F₅ — Constructive and digital

Digital (50, 95, 82)-net over F₅, using

t-expansion [i] based on digital (48, 95, 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]

(50, 50+45, 120)-Net over F₅ — Digital

Digital (50, 95, 120)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(50, 50+45, 2178)-Net in Base 5 — Upper bound on s

There is no (50, 95, 2179)-net in base 5, because

1 times m-reduction [i] would yield (50, 94, 2179)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 508077 939106 416072 439999 124516 838153 638109 727442 023532 407951 566505 > 5⁹⁴ [i]