MinT - Best Known (15, 15+39, s)-Nets in Base 5

Best Known (15, 15+39, s)-Nets in Base 5

(15, 15+39, 36)-Net over F₅ — Constructive and digital

Digital (15, 54, 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+39, 39)-Net over F₅ — Digital

Digital (15, 54, 39)-net over F₅, using

t-expansion [i] based on digital (14, 54, 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+39, 156)-Net in Base 5 — Upper bound on s

There is no (15, 54, 157)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁵⁴, 157, S₅, 39), but
- the linear programming bound shows that MÂ â‰¥ 278713 627224 633547 271796 867438 967703 332332 899627 718537 583932 629786 431789 398193 359375 000000 / 4866 358615 630033 040600 091027 258825 202934 788811 083799 > 5⁵⁴ [i]