MinT - Best Known (72, 72+57, s)-Nets in Base 16

Best Known (72, 72+57, s)-Nets in Base 16

(72, 72+57, 528)-Net over F₁₆ — Constructive and digital

Digital (72, 129, 528)-net over F₁₆, using

1 times m-reduction [i] based on digital (72, 130, 528)-net over F₁₆, using
- trace code for nets [i] based on digital (7, 65, 264)-net over F₂₅₆, using
  - net from sequence [i] based on digital (7, 263)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(72, 72+57, 876)-Net over F₁₆ — Digital

Digital (72, 129, 876)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+57, 240676)-Net in Base 16 — Upper bound on s

There is no (72, 129, 240677)-net in base 16, because

1 times m-reduction [i] would yield (72, 128, 240677)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 13407 854912 130371 379464 622191 718157 602368 014359 242443 998197 514819 688027 367579 530306 950974 865930 130003 302811 570297 389129 942954 688247 090793 605068 982086 256116 > 16¹²⁸ [i]