MinT - Best Known (125, 230, s)-Nets in Base 2

Best Known (125, 230, s)-Nets in Base 2

(125, 230, 62)-Net over F₂ — Constructive and digital

Digital (125, 230, 62)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (19, 71, 20)-net over F₂, using
  - net from sequence [i] based on digital (19, 19)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
      - an explicitly constructive algebraic function field [i]
2. digital (54, 159, 42)-net over F₂, using
  - net from sequence [i] based on digital (54, 41)-sequence over F₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
      - an explicitly constructive algebraic function field [i]

(125, 230, 80)-Net over F₂ — Digital

Digital (125, 230, 80)-net over F₂, using

t-expansion [i] based on digital (121, 230, 80)-net over F₂, using
- net from sequence [i] based on digital (121, 79)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 121 and N(F) ≥ 80, using
    - Drinfeld modules of rank 1 [i]

(125, 230, 276)-Net in Base 2 — Upper bound on s

There is no (125, 230, 277)-net in base 2, because

1 times m-reduction [i] would yield (125, 229, 277)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2²²⁹, 277, S₂, 104), but
  - the linear programming bound shows that MÂ â‰¥ 288 210741 112781 803449 096818 045883 935285 349639 863224 227722 405271 447495 793972 948510 965760 / 328748 659445 352861 > 2²²⁹ [i]