MinT - Best Known (98−59, 98, s)-Nets in Base 5

Best Known (98−59, 98, s)-Nets in Base 5

(98−59, 98, 78)-Net over F₅ — Constructive and digital

Digital (39, 98, 78)-net over F₅, using

t-expansion [i] based on digital (38, 98, 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]

(98−59, 98, 614)-Net in Base 5 — Upper bound on s

There is no (39, 98, 615)-net in base 5, because

1 times m-reduction [i] would yield (39, 97, 615)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 65 080239 169276 881109 700557 788302 717811 011087 287047 715789 485901 483821 > 5⁹⁷ [i]