MinT - Best Known (243−85, 243, s)-Nets in Base 2

Best Known (243−85, 243, s)-Nets in Base 2

(243−85, 243, 112)-Net over F₂ — Constructive and digital

Digital (158, 243, 112)-net over F₂, using

7 times m-reduction [i] based on digital (158, 250, 112)-net over F₂, using
- trace code for nets [i] based on digital (33, 125, 56)-net over F₄, using
  - net from sequence [i] based on digital (33, 55)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
      - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(243−85, 243, 148)-Net over F₂ — Digital

Digital (158, 243, 148)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−85, 243, 835)-Net in Base 2 — Upper bound on s

There is no (158, 243, 836)-net in base 2, because

1 times m-reduction [i] would yield (158, 242, 836)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 261226 735959 811433 416193 366362 919754 323123 889318 873076 365639 432330 051160 > 2²⁴² [i]