MinT - Best Known (90, 150, s)-Nets in Base 5

Best Known (90, 150, s)-Nets in Base 5

(90, 150, 252)-Net over F₅ — Constructive and digital

Digital (90, 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]

(90, 150, 320)-Net over F₅ — Digital

Digital (90, 150, 320)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 150, 9387)-Net in Base 5 — Upper bound on s

There is no (90, 150, 9388)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 701 136996 919451 430167 482203 216029 914122 838951 176610 158458 324977 385149 590688 129694 728580 281085 916193 762625 > 5¹⁵⁰ [i]