MinT - Best Known (242−88, 242, s)-Nets in Base 2

Best Known (242−88, 242, s)-Nets in Base 2

(242−88, 242, 112)-Net over F₂ — Constructive and digital

Digital (154, 242, 112)-net over F₂, using

trace code for nets [i] based on digital (33, 121, 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]

(242−88, 242, 135)-Net over F₂ — Digital

Digital (154, 242, 135)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−88, 242, 717)-Net in Base 2 — Upper bound on s

There is no (154, 242, 718)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 7 150888 458026 590733 085582 941471 519183 084359 540096 095973 719084 671702 847090 > 2²⁴² [i]