MinT - Best Known (15, 15+40, s)-Nets in Base 5

Best Known (15, 15+40, s)-Nets in Base 5

(15, 15+40, 36)-Net over F₅ — Constructive and digital

Digital (15, 55, 36)-net over F₅, using

net from sequence [i] based on digital (15, 35)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₅ with g(F)Â =Â 11, N(F)Â =Â 32, and 4 places with degree 2 [i] based on function field F/F₅ with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]

(15, 15+40, 39)-Net over F₅ — Digital

Digital (15, 55, 39)-net over F₅, using

t-expansion [i] based on digital (14, 55, 39)-net over F₅, using
- net from sequence [i] based on digital (14, 38)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 14 and N(F) ≥ 39, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(15, 15+40, 153)-Net in Base 5 — Upper bound on s

There is no (15, 55, 154)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵⁵, 154, S₅, 40), but
- the linear programming bound shows that MÂ â‰¥ 630 930266 838747 698612 633514 784160 850761 787398 571643 864266 792264 886460 930028 988514 095544 815063 476562 500000 / 2 156935 967408 873107 944147 762262 827160 214353 779709 131844 415112 471431 > 5⁵⁵ [i]