MinT - Best Known (135−99, 135, s)-Nets in Base 2

Best Known (135−99, 135, s)-Nets in Base 2

(135−99, 135, 24)-Net over F₂ — Constructive and digital

Digital (36, 135, 24)-net over F₂, using

t-expansion [i] based on digital (33, 135, 24)-net over F₂, using
- net from sequence [i] based on digital (33, 23)-sequence over F₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 33 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(135−99, 135, 30)-Net over F₂ — Digital

Digital (36, 135, 30)-net over F₂, using

net from sequence [i] based on digital (36, 29)-sequence over F₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂ with g(F) = 36 and N(F) ≥ 30, using
  - Drinfeld modules of rank 1 [i]

(135−99, 135, 56)-Net in Base 2 — Upper bound on s

There is no (36, 135, 57)-net in base 2, because

28 times m-reduction [i] would yield (36, 107, 57)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2¹⁰⁷, 57, S₂, 2, 71), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 649 037107 316853 453566 312041 152512 / 3 > 2¹⁰⁷ [i]