MinT - Best Known (18, 18+88, s)-Nets in Base 7

Best Known (18, 18+88, s)-Nets in Base 7

(18, 18+88, 26)-Net over F₇ — Constructive and digital

Digital (18, 106, 26)-net over F₇, using

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

(18, 18+88, 51)-Net over F₇ — Digital

Digital (18, 106, 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+88, 143)-Net in Base 7 — Upper bound on s

There is no (18, 106, 144)-net in base 7, because

extracting embedded orthogonal array [i] would yield OA(7¹⁰⁶, 144, S₇, 88), but
- the linear programming bound shows that MÂ â‰¥ 709 689323 561944 770400 558490 528209 672098 697718 160385 208241 993321 697408 165166 096960 368397 925749 319449 170279 411563 272677 630241 040333 425287 / 1800 025338 196749 580263 193678 780830 773760 000000 > 7¹⁰⁶ [i]