MinT - Best Known (66, 66+36, s)-Nets in Base 5

Best Known (66, 66+36, s)-Nets in Base 5

(66, 66+36, 252)-Net over F₅ — Constructive and digital

Digital (66, 102, 252)-net over F₅, using

10 times m-reduction [i] based on digital (66, 112, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 56, 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]

(66, 66+36, 383)-Net over F₅ — Digital

Digital (66, 102, 383)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+36, 17241)-Net in Base 5 — Upper bound on s

There is no (66, 102, 17242)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 197336 109047 351449 644048 019742 892740 071893 991001 356512 496084 654984 076225 > 5¹⁰² [i]