MinT - Best Known (236−131, 236, s)-Nets in Base 2

Best Known (236−131, 236, s)-Nets in Base 2

(236−131, 236, 56)-Net over F₂ — Constructive and digital

Digital (105, 236, 56)-net over F₂, using

net from sequence [i] based on digital (105, 55)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₂ with g(F)Â =Â 69, N(F)Â =Â 48, 1 place with degree 2, and 7 places with degree 6 [i] based on function field F/F₂ with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]

(236−131, 236, 65)-Net over F₂ — Digital

Digital (105, 236, 65)-net over F₂, using

t-expansion [i] based on digital (95, 236, 65)-net over F₂, using
- net from sequence [i] based on digital (95, 64)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 95 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

(236−131, 236, 221)-Net in Base 2 — Upper bound on s

There is no (105, 236, 222)-net in base 2, because

1 times m-reduction [i] would yield (105, 235, 222)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 55892 468183 512935 753741 207327 737684 869031 217673 977244 560480 274515 606869 > 2²³⁵ [i]