MinT - Best Known (111−87, 111, s)-Nets in Base 5

Best Known (111−87, 111, s)-Nets in Base 5

(111−87, 111, 51)-Net over F₅ — Constructive and digital

Digital (24, 111, 51)-net over F₅, using

t-expansion [i] based on digital (22, 111, 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]

(111−87, 111, 55)-Net over F₅ — Digital

Digital (24, 111, 55)-net over F₅, using

t-expansion [i] based on digital (23, 111, 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]

(111−87, 111, 125)-Net in Base 5 — Upper bound on s

There is no (24, 111, 126)-net in base 5, because

3 times m-reduction [i] would yield (24, 108, 126)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5¹⁰⁸, 126, S₅, 84), but
  - the linear programming bound shows that MÂ â‰¥ 2 094092 513870 288705 839493 432161 771605 009517 271370 374225 103461 185426 567681 133747 100830 078125 / 654 802567 287869 > 5¹⁰⁸ [i]