MinT - Best Known (43−33, 43, s)-Nets in Base 5

Best Known (43−33, 43, s)-Nets in Base 5

(43−33, 43, 26)-Net over F₅ — Constructive and digital

Digital (10, 43, 26)-net over F₅, using

t-expansion [i] based on digital (9, 43, 26)-net over F₅, using
- net from sequence [i] based on digital (9, 25)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 9 and N(F) ≥ 26, using
    - an explicitly constructive algebraic function field [i]

(43−33, 43, 27)-Net over F₅ — Digital

Digital (10, 43, 27)-net over F₅, using

net from sequence [i] based on digital (10, 26)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 10 and N(F) ≥ 27, using
  - algebraic function fields over â„¤₅ by Niederreiter/Xing [i]

(43−33, 43, 93)-Net in Base 5 — Upper bound on s

There is no (10, 43, 94)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴³, 94, S₅, 33), but
- the linear programming bound shows that MÂ â‰¥ 74027 324289 935765 202380 954965 530220 573940 762942 077554 984915 701753 898105 152984 499000 012874 603271 484375 / 60404 659009 312722 473429 997580 777486 179967 377412 005642 674492 888938 351871 > 5⁴³ [i]