MinT - Best Known (236−138, 236, s)-Nets in Base 2

Best Known (236−138, 236, s)-Nets in Base 2

(236−138, 236, 54)-Net over F₂ — Constructive and digital

Digital (98, 236, 54)-net over F₂, using

t-expansion [i] based on digital (95, 236, 54)-net over F₂, using
- net from sequence [i] based on digital (95, 53)-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 5 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]

(236−138, 236, 65)-Net over F₂ — Digital

Digital (98, 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]

(236−138, 236, 195)-Net in Base 2 — Upper bound on s

There is no (98, 236, 196)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 131188 692037 508949 517963 355184 338877 460718 710164 303560 639153 308317 009208 > 2²³⁶ [i]