MinT - Best Known (133−37, 133, s)-Nets in Base 5

Best Known (133−37, 133, s)-Nets in Base 5

(133−37, 133, 400)-Net over F₅ — Constructive and digital

Digital (96, 133, 400)-net over F₅, using

9 times m-reduction [i] based on digital (96, 142, 400)-net over F₅, using
- trace code for nets [i] based on digital (25, 71, 200)-net over F₂₅, using
  - net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
      - a function field by GarcÃa and Quoos [i]

(133−37, 133, 1382)-Net over F₅ — Digital

Digital (96, 133, 1382)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−37, 133, 252247)-Net in Base 5 — Upper bound on s

There is no (96, 133, 252248)-net in base 5, because

1 times m-reduction [i] would yield (96, 132, 252248)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 183 671109 836836 252942 400413 973441 194811 012421 837214 354081 588398 356864 817068 008104 052417 554305 > 5¹³² [i]