MinT - Best Known (79−33, 79, s)-Nets in Base 16

Best Known (79−33, 79, s)-Nets in Base 16

(79−33, 79, 526)-Net over F₁₆ — Constructive and digital

Digital (46, 79, 526)-net over F₁₆, using

1 times m-reduction [i] based on digital (46, 80, 526)-net over F₁₆, using
- trace code for nets [i] based on digital (6, 40, 263)-net over F₂₅₆, using
  - net from sequence [i] based on digital (6, 262)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(79−33, 79, 817)-Net over F₁₆ — Digital

Digital (46, 79, 817)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(79−33, 79, 336140)-Net in Base 16 — Upper bound on s

There is no (46, 79, 336141)-net in base 16, because

1 times m-reduction [i] would yield (46, 78, 336141)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 8343 753049 007642 380190 878774 607100 397422 879617 126907 542298 450172 911207 016563 377493 252136 195216 > 16⁷⁸ [i]