MinT - Best Known (44, 44+62, s)-Nets in Base 5

Best Known (44, 44+62, s)-Nets in Base 5

(44, 44+62, 78)-Net over F₅ — Constructive and digital

Digital (44, 106, 78)-net over F₅, using

t-expansion [i] based on digital (38, 106, 78)-net over F₅, using
- net from sequence [i] based on digital (38, 77)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
    - an explicitly constructive algebraic function field [i]

(44, 44+62, 84)-Net over F₅ — Digital

Digital (44, 106, 84)-net over F₅, using

t-expansion [i] based on digital (43, 106, 84)-net over F₅, using
- net from sequence [i] based on digital (43, 83)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 43 and N(F) ≥ 84, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(44, 44+62, 739)-Net in Base 5 — Upper bound on s

There is no (44, 106, 740)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 125 446518 539377 202566 108422 500574 034388 659627 041685 195783 488498 727499 070993 > 5¹⁰⁶ [i]