MinT - Best Known (89, 89+59, s)-Nets in Base 5

Best Known (89, 89+59, s)-Nets in Base 5

(89, 89+59, 252)-Net over F₅ — Constructive and digital

Digital (89, 148, 252)-net over F₅, using

t-expansion [i] based on digital (85, 148, 252)-net over F₅, using
- 2 times m-reduction [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]

(89, 89+59, 320)-Net over F₅ — Digital

Digital (89, 148, 320)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(89, 89+59, 10167)-Net in Base 5 — Upper bound on s

There is no (89, 148, 10168)-net in base 5, because

1 times m-reduction [i] would yield (89, 147, 10168)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 5 614429 536888 983847 720876 075534 889340 754257 231809 752987 683283 560681 509349 300010 222917 430662 486691 659745 > 5¹⁴⁷ [i]