MinT - Best Known (116−43, 116, s)-Nets in Base 5

Best Known (116−43, 116, s)-Nets in Base 5

(116−43, 116, 252)-Net over F₅ — Constructive and digital

Digital (73, 116, 252)-net over F₅, using

10 times m-reduction [i] based on digital (73, 126, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 63, 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]

(116−43, 116, 345)-Net over F₅ — Digital

Digital (73, 116, 345)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−43, 116, 14577)-Net in Base 5 — Upper bound on s

There is no (73, 116, 14578)-net in base 5, because

1 times m-reduction [i] would yield (73, 115, 14578)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 241 048695 514592 617185 380642 632074 391217 555371 239282 976800 491562 328464 675519 775945 > 5¹¹⁵ [i]