MinT - Best Known (24, 102, s)-Nets in Base 5

Best Known (24, 102, s)-Nets in Base 5

(24, 102, 51)-Net over F₅ — Constructive and digital

Digital (24, 102, 51)-net over F₅, using

t-expansion [i] based on digital (22, 102, 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]

(24, 102, 55)-Net over F₅ — Digital

Digital (24, 102, 55)-net over F₅, using

t-expansion [i] based on digital (23, 102, 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]

(24, 102, 135)-Net in Base 5 — Upper bound on s

There is no (24, 102, 136)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5¹⁰², 136, S₅, 78), but
- the linear programming bound shows that MÂ â‰¥ 57647 613224 889334 270126 424960 601803 968793 830856 856227 375095 702569 751665 578223 764896 392822 265625 / 270494 125252 812747 014144 > 5¹⁰² [i]