MinT - Best Known (115−90, 115, s)-Nets in Base 5

Best Known (115−90, 115, s)-Nets in Base 5

(115−90, 115, 51)-Net over F₅ — Constructive and digital

Digital (25, 115, 51)-net over F₅, using

t-expansion [i] based on digital (22, 115, 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]

(115−90, 115, 55)-Net over F₅ — Digital

Digital (25, 115, 55)-net over F₅, using

t-expansion [i] based on digital (23, 115, 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]

(115−90, 115, 129)-Net in Base 5 — Upper bound on s

There is no (25, 115, 130)-net in base 5, because

1 times m-reduction [i] would yield (25, 114, 130)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(5¹¹⁴, 130, S₅, 89), but
  - the linear programming bound shows that MÂ â‰¥ 2 714752 481472 636819 003446 408307 138614 112384 082080 638159 073515 680574 928410 351276 397705 078125 / 40501 705629 > 5¹¹⁴ [i]