MinT - Best Known (10, 10+36, s)-Nets in Base 5

Best Known (10, 10+36, s)-Nets in Base 5

(10, 10+36, 26)-Net over F₅ — Constructive and digital

Digital (10, 46, 26)-net over F₅, using

t-expansion [i] based on digital (9, 46, 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]

(10, 10+36, 27)-Net over F₅ — Digital

Digital (10, 46, 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]

(10, 10+36, 79)-Net in Base 5 — Upper bound on s

There is no (10, 46, 80)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁴⁶, 80, S₅, 36), but
- the linear programming bound shows that MÂ â‰¥ 77170 340181 070590 961945 521665 722993 838468 820371 190304 285846 650600 433349 609375 / 522 365409 226884 536298 358374 879219 876117 346399 > 5⁴⁶ [i]