MinT - Best Known (4, 77, s)-Nets in Base 25

Best Known (4, 77, s)-Nets in Base 25

(4, 77, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 77, 66)-net over F₂₅, using

net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
  - a function field by GarcÃa and Quoos [i]

(4, 77, 296)-Net in Base 25 — Upper bound on s

There is no (4, 77, 297)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁷⁷, 297, S₂₅, 73), but
- the linear programming bound shows that MÂ â‰¥ 215100 833921 838455 682716 111513 443814 490692 132574 974923 865582 573796 889213 076096 247866 532187 196234 176553 531758 369075 532755 232416 093349 456787 109375 / 487293 233455 641173 257752 533849 012407 > 25⁷⁷ [i]