MinT - Best Known (78−29, 78, s)-Nets in Base 5

Best Known (78−29, 78, s)-Nets in Base 5

(78−29, 78, 252)-Net over F₅ — Constructive and digital

Digital (49, 78, 252)-net over F₅, using

trace code for nets [i] based on digital (10, 39, 126)-net over F₂₅, using
- net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]

(78−29, 78, 253)-Net over F₅ — Digital

Digital (49, 78, 253)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(78−29, 78, 10551)-Net in Base 5 — Upper bound on s

There is no (49, 78, 10552)-net in base 5, because

1 times m-reduction [i] would yield (49, 77, 10552)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 662027 178012 721251 981793 574915 266440 107845 539237 425025 > 5⁷⁷ [i]