MinT - Best Known (18, 18+87, s)-Nets in Base 7

Best Known (18, 18+87, s)-Nets in Base 7

(18, 18+87, 26)-Net over F₇ — Constructive and digital

Digital (18, 105, 26)-net over F₇, using

net from sequence [i] based on digital (18, 25)-sequence over F₇, using
- Niederreiter sequence [i]

(18, 18+87, 51)-Net over F₇ — Digital

Digital (18, 105, 51)-net over F₇, using

net from sequence [i] based on digital (18, 50)-sequence over F₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 18 and N(F) ≥ 51, using
  - an algebraic function field by Teo [i]

(18, 18+87, 146)-Net in Base 7 — Upper bound on s

There is no (18, 105, 147)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7¹⁰⁵, 147, S₇, 87), but
- the linear programming bound shows that MÂ â‰¥ 147 690405 180025 380122 216385 426592 249360 886576 681831 958995 619799 627596 195289 898545 868370 266432 169545 520270 550456 903791 210379 148307 790155 881587 / 2700 862948 334492 176361 502067 494535 228489 238723 805184 > 7¹⁰⁵ [i]