MinT - Best Known (91, 150, s)-Nets in Base 5

Best Known (91, 150, s)-Nets in Base 5

(91, 150, 252)-Net over F₅ — Constructive and digital

Digital (91, 150, 252)-net over F₅, using

t-expansion [i] based on digital (85, 150, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 75, 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]

(91, 150, 340)-Net over F₅ — Digital

Digital (91, 150, 340)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 150, 11363)-Net in Base 5 — Upper bound on s

There is no (91, 150, 11364)-net in base 5, because

1 times m-reduction [i] would yield (91, 149, 11364)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 140 320067 597113 585180 406453 122134 249588 743047 744627 916643 397968 068759 243510 943941 650818 447806 468575 254545 > 5¹⁴⁹ [i]