MinT - Best Known (126−97, 126, s)-Nets in Base 5

Best Known (126−97, 126, s)-Nets in Base 5

(126−97, 126, 51)-Net over F₅ — Constructive and digital

Digital (29, 126, 51)-net over F₅, using

t-expansion [i] based on digital (22, 126, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(126−97, 126, 56)-Net over F₅ — Digital

Digital (29, 126, 56)-net over F₅, using

net from sequence [i] based on digital (29, 55)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 29 and N(F) ≥ 56, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(126−97, 126, 149)-Net in Base 5 — Upper bound on s

There is no (29, 126, 150)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹²⁶, 150, S₅, 97), but
- the linear programming bound shows that MÂ â‰¥ 36 026079 456021 401807 410154 480760 438768 372858 795374 723787 651793 517725 247462 113458 141175 215132 534503 936767 578125 / 2872 765687 918138 939304 > 5¹²⁶ [i]