MinT - Best Known (114, 114+86, s)-Nets in Base 2

Best Known (114, 114+86, s)-Nets in Base 2

(114, 114+86, 60)-Net over F₂ — Constructive and digital

Digital (114, 200, 60)-net over F₂, using

2 times m-reduction [i] based on digital (114, 202, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 101, 30)-net over F₄, using
  - net from sequence [i] based on digital (13, 29)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
      - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(114, 114+86, 78)-Net over F₂ — Digital

Digital (114, 200, 78)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(114, 114+86, 298)-Net in Base 2 — Upper bound on s

There is no (114, 200, 299)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²⁰⁰, 299, S₂, 86), but
- adding a parity check bit [i] would yield OA(2²⁰¹, 300, S₂, 87), but
  - the linear programming bound shows that MÂ â‰¥ 6062 729839 358588 077129 287653 744482 312929 554681 473387 231550 995785 979703 893542 676711 534073 403563 590830 522368 / 1273 266655 863433 158102 727954 895995 795355 723661 > 2²⁰¹ [i]