MinT - Best Known (133−51, 133, s)-Nets in Base 5

Best Known (133−51, 133, s)-Nets in Base 5

(133−51, 133, 252)-Net over F₅ — Constructive and digital

Digital (82, 133, 252)-net over F₅, using

11 times m-reduction [i] based on digital (82, 144, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 72, 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]

(133−51, 133, 338)-Net over F₅ — Digital

Digital (82, 133, 338)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−51, 133, 12459)-Net in Base 5 — Upper bound on s

There is no (82, 133, 12460)-net in base 5, because

1 times m-reduction [i] would yield (82, 132, 12460)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 183 944929 356550 865695 947245 514726 890549 023071 351218 044072 554611 840618 287839 974180 339143 535537 > 5¹³² [i]