MinT - Best Known (25, 25+83, s)-Nets in Base 5

Best Known (25, 25+83, s)-Nets in Base 5

(25, 25+83, 51)-Net over F₅ — Constructive and digital

Digital (25, 108, 51)-net over F₅, using

t-expansion [i] based on digital (22, 108, 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]

(25, 25+83, 55)-Net over F₅ — Digital

Digital (25, 108, 55)-net over F₅, using

t-expansion [i] based on digital (23, 108, 55)-net over F₅, using
- net from sequence [i] based on digital (23, 54)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 23 and N(F) ≥ 55, using
    - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(25, 25+83, 134)-Net in Base 5 — Upper bound on s

There is no (25, 108, 135)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰⁸, 135, S₅, 83), but
- the linear programming bound shows that MÂ â‰¥ 19277 424638 975380 150762 835693 739866 028797 134088 660996 352471 155290 686510 852538 049221 038818 359375 / 5 879817 587577 865932 > 5¹⁰⁸ [i]