MinT - Best Known (106−89, 106, s)-Nets in Base 7

Best Known (106−89, 106, s)-Nets in Base 7

(106−89, 106, 25)-Net over F₇ — Constructive and digital

Digital (17, 106, 25)-net over F₇, using

net from sequence [i] based on digital (17, 24)-sequence over F₇, using
- Niederreiter sequence [i]

(106−89, 106, 48)-Net over F₇ — Digital

Digital (17, 106, 48)-net over F₇, using

t-expansion [i] based on digital (13, 106, 48)-net over F₇, using
- net from sequence [i] based on digital (13, 47)-sequence over F₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 13 and N(F) ≥ 48, using
    - an algebraic function field by Teo [i]

(106−89, 106, 123)-Net in Base 7 — Upper bound on s

There is no (17, 106, 124)-net in base 7, because

1 times m-reduction [i] would yield (17, 105, 124)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(7¹⁰⁵, 124, S₇, 88), but
  - the linear programming bound shows that MÂ â‰¥ 55343 783187 778079 903463 566814 152954 324006 357534 257980 122642 017813 136518 579676 966486 015223 475056 450788 682119 / 1 015487 950729 776875 > 7¹⁰⁵ [i]