MinT - Best Known (20, 20+68, s)-Nets in Base 5

Best Known (20, 20+68, s)-Nets in Base 5

(20, 20+68, 43)-Net over F₅ — Constructive and digital

Digital (20, 88, 43)-net over F₅, using

t-expansion [i] based on digital (18, 88, 43)-net over F₅, using
- net from sequence [i] based on digital (18, 42)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₅ with g(F)Â =Â 17, N(F)Â =Â 42, and 1 place with degree 2 [i] based on function field F/F₅ with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]

(20, 20+68, 45)-Net over F₅ — Digital

Digital (20, 88, 45)-net over F₅, using

t-expansion [i] based on digital (19, 88, 45)-net over F₅, using
- net from sequence [i] based on digital (19, 44)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 19 and N(F) ≥ 45, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(20, 20+68, 113)-Net in Base 5 — Upper bound on s

There is no (20, 88, 114)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁸⁸, 114, S₅, 68), but
- the linear programming bound shows that MÂ â‰¥ 875 158600 035130 718590 193114 166978 256428 415516 854357 747433 823533 356189 727783 203125 / 22 570271 614906 058421 > 5⁸⁸ [i]