MinT - Best Known (72, 72+51, s)-Nets in Base 16

Best Known (72, 72+51, s)-Nets in Base 16

(72, 72+51, 534)-Net over F₁₆ — Constructive and digital

Digital (72, 123, 534)-net over F₁₆, using

1 times m-reduction [i] based on digital (72, 124, 534)-net over F₁₆, using
- trace code for nets [i] based on digital (10, 62, 267)-net over F₂₅₆, using
  - net from sequence [i] based on digital (10, 266)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(72, 72+51, 1215)-Net over F₁₆ — Digital

Digital (72, 123, 1215)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+51, 510068)-Net in Base 16 — Upper bound on s

There is no (72, 123, 510069)-net in base 16, because

1 times m-reduction [i] would yield (72, 122, 510069)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 799 189816 865461 140195 615282 144308 407917 660943 738844 074056 811436 231257 122577 792377 330114 888935 901621 638004 000854 653647 210644 211066 312096 848780 163376 > 16¹²² [i]