MinT - Best Known (98−76, 98, s)-Nets in Base 5

Best Known (98−76, 98, s)-Nets in Base 5

(98−76, 98, 51)-Net over F₅ — Constructive and digital

Digital (22, 98, 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]

(98−76, 98, 118)-Net in Base 5 — Upper bound on s

There is no (22, 98, 119)-net in base 5, because

extracting embedded orthogonal array [i] would yield OA(5⁹⁸, 119, S₅, 76), but
- the linear programming bound shows that MÂ â‰¥ 329925 329715 815493 212685 704525 339993 066208 703342 834240 856973 337940 871715 545654 296875 / 783 804970 239291 > 5⁹⁸ [i]