MinT - Best Known (4, 79, s)-Nets in Base 25

Best Known (4, 79, s)-Nets in Base 25

(4, 79, 66)-Net over F₂₅ — Constructive and digital

Digital (4, 79, 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, 79, 279)-Net in Base 25 — Upper bound on s

There is no (4, 79, 280)-net in base 25, because

extracting embedded orthogonal array [i] would yield OA(25⁷⁹, 280, S₂₅, 75), but
- the linear programming bound shows that MÂ â‰¥ 199977 162596 644996 946120 394131 181546 300766 968985 601844 143776 216677 846096 697812 318596 109803 694310 775444 806000 007702 539988 940770 854242 146015 167236 328125 / 708 956488 393352 111362 217329 311570 317668 > 25⁷⁹ [i]