MinT - Best Known (86, 86+64, s)-Nets in Base 5

Best Known (86, 86+64, s)-Nets in Base 5

(86, 86+64, 252)-Net over F₅ — Constructive and digital

Digital (86, 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]

(86, 86+64, 253)-Net over F₅ — Digital

Digital (86, 150, 253)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 86+64, 6019)-Net in Base 5 — Upper bound on s

There is no (86, 150, 6020)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 702 919789 203281 300976 911622 131833 888611 061865 740615 638243 629282 189013 818705 615307 212724 789550 441518 956545 > 5¹⁵⁰ [i]