MinT - Best Known (116, 116+88, s)-Nets in Base 2

Best Known (116, 116+88, s)-Nets in Base 2

(116, 116+88, 60)-Net over F₂ — Constructive and digital

Digital (116, 204, 60)-net over F₂, using

2 times m-reduction [i] based on digital (116, 206, 60)-net over F₂, using
- trace code for nets [i] based on digital (13, 103, 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]

(116, 116+88, 79)-Net over F₂ — Digital

Digital (116, 204, 79)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+88, 298)-Net in Base 2 — Upper bound on s

There is no (116, 204, 299)-net in base 2, because

extracting embedded orthogonal array [i] would yield OA(2²⁰⁴, 299, S₂, 88), but
- adding a parity check bit [i] would yield OA(2²⁰⁵, 300, S₂, 89), but
  - the linear programming bound shows that MÂ â‰¥ 416927 463188 475542 795463 940731 898983 181308 104641 213119 598295 609827 594303 154474 074874 094714 331435 368448 / 5584 401256 756961 297780 513782 298869 514125 > 2²⁰⁵ [i]