MinT - Best Known (77, 77+69, s)-Nets in Base 5

Best Known (77, 77+69, s)-Nets in Base 5

(77, 77+69, 132)-Net over F₅ — Constructive and digital

Digital (77, 146, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 73, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(77, 77+69, 173)-Net over F₅ — Digital

Digital (77, 146, 173)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+69, 3213)-Net in Base 5 — Upper bound on s

There is no (77, 146, 3214)-net in base 5, because

1 times m-reduction [i] would yield (77, 145, 3214)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 225701 294866 667249 448560 582693 779272 497372 397406 795943 114843 411165 050378 119463 211123 675017 944427 757825 > 5¹⁴⁵ [i]